It puts the ip address for the site mentioned in the screenshot in your computers dns lookup table. For when they kill the global dns cache and block dns lookups to block said site. It will basically allow you to still access that site without having to perform the dns lookup. Think of a web url as a name in a phone book, with the ip address being the associated phone number. When you navigate to a url, your device hits up a dns server to see what the "phone number" is before sending your request to the ipaddress by url. They have the ability to remove all or select names from the phone book. Rendering a dns lookup useless, and thus preventing you from accessing the site at the ip address. By adding these entries to your host file it will go straight there, without having to get the ip address from a dns server. Effectively bypassing their girlyman attempts to keep you from accessing certain sites.

If the DS does shutdown the worldwide DNS system, or if they just delete entries for the conservative sites, you can set up a home DNS server in advance that can maintain the missing dns entries to keep you online. Here’s an easy one for Windows Macines https://simpledns.plus/ and linux machines would need to use something like DNSMasq.

Instead of a full dns server, you may be able to just point your dns server to one of these special purpose dns server, as long as they aren’t poisoned too, but we won’t know that until SHTF day. It info worth holding onto until that day tho. https://www.lifewire.com/free-and-public-dns-servers-2626062